One Solution collect form web for “Can a GIT branch have a subset of data?”

One way would be to export the history of that webapp directory an an independent git repo, used within the current (parent) repo as a submodule.
That way, you are sure the external contributor doesn’t modify any source except the ones you want.

The other (simpler) way is to create a branch dedicated for the other group of contributors, and accept merges only through pull request (that you would reject if any file outside of webapp is modified)